Superconducting proximity effect in quantum wires without time-reversal symmetry

Abstract

We study the superconducting proximity effect in a quantum wire with broken time-reversal (TR) symmetry connected to a conventional superconductor. We consider the situation of a strong TR-symmetry breaking, so that Cooper pairs entering the wire from the superconductor are immediately destroyed. Nevertheless, some traces of the proximity effect survive: for example, the local electronic density of states (LDOS) is influenced by the proximity to the superconductor, provided that localization effects are taken into account. With the help of the supersymmetric sigma model, we calculate the average LDOS in such a system. The LDOS in the wire is strongly modified close to the interface with the superconductor at energies near the Fermi level. The relevant distances from the interface are of the order of the localization length, and the size of the energy window around the Fermi level is of the order of the mean level spacing at the localization length. Remarkably, the sign of the effect is sensitive to the way the TR symmetry is broken: In the spin-symmetric case (orbital magnetic field), the LDOS is depleted near the Fermi energy, whereas for the broken spin symmetry (magnetic impurities), the LDOS at the Fermi energy is enhanced.